Which one of the following is one of the factors of x2 (y – z) + y2

1.	Which one of the following is one of the factors of x2 (y – z) + y2 (z – x) – z (xy – yz – zx) ?(a) (x – y) (b) (x + y – z) (c) (x – y – z) (d) (x + y + z)
Answer» (c) (x – y – z) x² (y – z) + y² (z – x) – z(xy – yz – zx) = x²y – x²z + y²z – y²x – zxy + yz² + z²x = xy(x – y – z) + z²(x + y) – z (x² – y²) = xy(x – y – z) – z (x + y) (x – y – z) = (x – y – z) (xy – yz – zx) Hence, (c) is the correct option.

Which one of the following is one of the factors of x2 (y – z) + y2 (z – x) – z (xy – yz – zx) ?(a) (x – y) (b) (x + y – z) (c) (x – y – z) (d) (x + y + z)

Answer»

(c) (x – y – z)

x² (y – z) + y² (z – x) – z(xy – yz – zx)

= x²y – x²z + y²z – y²x – zxy + yz² + z²x

= xy(x – y – z) + z²(x + y) – z (x² – y²)

= xy(x – y – z) – z (x + y) (x – y – z) = (x – y – z) (xy – yz – zx)

Hence, (c) is the correct option.